Answer:
[tex]\sqrt[]{\frac{x+8}{4}}-3[/tex]
Step-by-step explanation:
[tex]g(x)=4(x+3)^2-8[/tex]
First rewrite [tex]g(x)[/tex] as y
[tex]y=4(x+3)^2-8[/tex]
Now swap y and x
[tex]x=4(y+3)^2-8[/tex]
Add 8 on both sides.
[tex]x+8=4(y+3)^2-8+8[/tex]
[tex]x+8=4(y+3)^2[/tex]
Divide by 4.
[tex]\frac{x+8}{4} =\frac{4(y+3)^2}{4}[/tex]
[tex]\frac{x+8}{4}=(y+3)^2[/tex]
Extract the square root on both sides.
[tex]\sqrt[]{\frac{x+8}{4}}=\sqrt[]{(y+3)^2}[/tex]
[tex]\sqrt[]{\frac{x+8}{4}}=y+3[/tex]
Subtract 3 on both sides.
[tex]\sqrt[]{\frac{x+8}{4}}-3=y+3-3[/tex]
[tex]\sqrt[]{\frac{x+8}{4}}-3=y[/tex]
